scholarly journals Molecules Associated to Hardy Spaces with Pointwise Variable Anisotropy

2017 ◽  
Vol 89 (3) ◽  
pp. 301-313
Author(s):  
Víctor Almeida ◽  
Jorge J. Betancor ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Hardy Spaces ◽  
Variable Anisotropy

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

scholarly journals Maximal Function Characterizations of Hardy Spaces on Rn with Pointwise Variable Anisotropy

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3246
Author(s):  
Aiting Wang ◽  
Wenhua Wang ◽  
Baode Li
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Full Range ◽  
Real Variable ◽  
Maximal Functions ◽  
High Anisotropy ◽  
Multi Level ◽  
Point To Point ◽  
Variable Anisotropy

In 2011, Dekel et al. developed highly geometric Hardy spaces Hp(Θ), for the full range 0<p≤1, which were constructed by continuous multi-level ellipsoid covers Θ of Rn with high anisotropy in the sense that the ellipsoids can rapidly change shape from point to point and from level to level. In this article, when the ellipsoids in Θ rapidly change shape from level to level, the authors further obtain some real-variable characterizations of Hp(Θ) in terms of the radial, the non-tangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

Hardy Spaces on ℝ n with Pointwise Variable Anisotropy

2011 ◽  
Vol 17 (5) ◽  
pp. 1066-1107 ◽  
Author(s):  
Shai Dekel ◽  
Pencho Petrushev ◽  
Tal Weissblat
Keyword(s):  
Hardy Spaces ◽  
Variable Anisotropy

HARDY SPACES, APPROXIMATION ISSUES AND BOUNDARY VALUE PROBLEMS

2018 ◽  
Vol 9 (3) ◽  
pp. 85-94
Author(s):  
V.I. Vlasov ◽  
◽  
◽  
Keyword(s):  
Boundary Value Problems ◽  
Hardy Spaces ◽  
Boundary Value

Fourier transform of anisotropic mixed-norm Hardy spaces

2021 ◽  
Vol 16 (1) ◽  
pp. 119-139
Author(s):  
Long Huang ◽  
Der-Chen Chang ◽  
Dachun Yang
Keyword(s):  
Fourier Transform ◽  
Hardy Spaces ◽  
Mixed Norm

Multi-parameter hardy spaces via discrete Littlewood-Paley theory

2010 ◽  
Vol 26 (2) ◽  
pp. 122-139 ◽  
Author(s):  
Zhuoping Ruan
Keyword(s):  
Hardy Spaces

Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 919-936 ◽  
Author(s):  
Jiao Chen ◽  
Wei Ding ◽  
Guozhen Lu
Keyword(s):  
Hardy Spaces ◽  
Differential Operators ◽  
Integral Operators ◽  
Fourier Multipliers ◽  
Regularity Of Solutions ◽  
Local Version ◽  
Fourier Integral Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces ◽  
The One

AbstractAfter the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity of solutions to PDEs such as the {\overline{\partial}} problem. The study of Fourier multipliers, pseudo-differential operators and Fourier integral operators has stimulated further such applications. It is well known that the one-parameter pseudo-differential operators are {L^{p}({\mathbb{R}^{n}})} bounded for {1<p<\infty}, but only bounded on local Hardy spaces {h^{p}({\mathbb{R}^{n}})} introduced by Goldberg in [D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 1979, 1, 27–42] for {0<p\leq 1}. Though much work has been done on the {L^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {1<p<\infty} and Hardy {H^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {0<p\leq 1} for multi-parameter Fourier multipliers and singular integral operators, not much has been done yet for the boundedness of multi-parameter pseudo-differential operators in the range of {0<p\leq 1}. The main purpose of this paper is to establish the boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} for {0<p\leq 1} recently introduced by Ding, Lu and Zhu in [W. Ding, G. Lu and Y. Zhu, Multi-parameter local Hardy spaces, Nonlinear Anal. 184 2019, 352–380].

Some Characterization of Herz and Herz-Type Hardy Spaces for the Dunkl Operator

2020 ◽  
Vol 51 (4) ◽  
pp. 1533-1554
Author(s):  
Mehdi Lachiheb ◽  
Abdesselem Gasmi
Keyword(s):  
Hardy Spaces ◽  
Dunkl Operator
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